3.5.100 \(\int \frac {-2 x^2+(-1+x) \log (4)+x \log (30)}{x} \, dx\)

Optimal. Leaf size=22 \[ x \left (-x+\log (30)-\frac {\log (4) (7-x+\log (x))}{x}\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 16, normalized size of antiderivative = 0.73, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {14} \begin {gather*} -x^2+x \log (120)-\log (4) \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-2*x^2 + (-1 + x)*Log[4] + x*Log[30])/x,x]

[Out]

-x^2 + x*Log[120] - Log[4]*Log[x]

Rule 14

Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x], x] /; FreeQ[{c, m}, x] && SumQ[u]
&&  !LinearQ[u, x] &&  !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-2 x-\frac {\log (4)}{x}+\log (120)\right ) \, dx\\ &=-x^2+x \log (120)-\log (4) \log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 16, normalized size = 0.73 \begin {gather*} -x^2+x \log (120)-\log (4) \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-2*x^2 + (-1 + x)*Log[4] + x*Log[30])/x,x]

[Out]

-x^2 + x*Log[120] - Log[4]*Log[x]

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fricas [A]  time = 0.87, size = 21, normalized size = 0.95 \begin {gather*} -x^{2} + x \log \left (30\right ) + 2 \, x \log \relax (2) - 2 \, \log \relax (2) \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x*log(30)+2*(x-1)*log(2)-2*x^2)/x,x, algorithm="fricas")

[Out]

-x^2 + x*log(30) + 2*x*log(2) - 2*log(2)*log(x)

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giac [A]  time = 0.56, size = 22, normalized size = 1.00 \begin {gather*} -x^{2} + x \log \left (30\right ) + 2 \, x \log \relax (2) - 2 \, \log \relax (2) \log \left ({\left | x \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x*log(30)+2*(x-1)*log(2)-2*x^2)/x,x, algorithm="giac")

[Out]

-x^2 + x*log(30) + 2*x*log(2) - 2*log(2)*log(abs(x))

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maple [A]  time = 0.04, size = 22, normalized size = 1.00

method	result	size
default	\(-x^{2}+2 x \ln \relax (2)+x \ln \left (30\right )-2 \ln \relax (2) \ln \relax (x )\)	\(22\)
norman	\(\left (2 \ln \relax (2)+\ln \left (30\right )\right ) x -x^{2}-2 \ln \relax (2) \ln \relax (x )\)	\(22\)
risch	\(3 x \ln \relax (2)+x \ln \relax (3)+x \ln \relax (5)-x^{2}-2 \ln \relax (2) \ln \relax (x )\)	\(26\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x*ln(30)+2*(x-1)*ln(2)-2*x^2)/x,x,method=_RETURNVERBOSE)

[Out]

-x^2+2*x*ln(2)+x*ln(30)-2*ln(2)*ln(x)

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maxima [A]  time = 0.37, size = 21, normalized size = 0.95 \begin {gather*} -x^{2} + x {\left (\log \left (30\right ) + 2 \, \log \relax (2)\right )} - 2 \, \log \relax (2) \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x*log(30)+2*(x-1)*log(2)-2*x^2)/x,x, algorithm="maxima")

[Out]

-x^2 + x*(log(30) + 2*log(2)) - 2*log(2)*log(x)

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mupad [B]  time = 0.06, size = 16, normalized size = 0.73 \begin {gather*} x\,\ln \left (120\right )-2\,\ln \relax (2)\,\ln \relax (x)-x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x*log(30) + 2*log(2)*(x - 1) - 2*x^2)/x,x)

[Out]

x*log(120) - 2*log(2)*log(x) - x^2

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sympy [A]  time = 0.10, size = 24, normalized size = 1.09 \begin {gather*} - x^{2} - x \left (- \log {\left (30 \right )} - 2 \log {\relax (2 )}\right ) - 2 \log {\relax (2 )} \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x*ln(30)+2*(x-1)*ln(2)-2*x**2)/x,x)

[Out]

-x**2 - x*(-log(30) - 2*log(2)) - 2*log(2)*log(x)

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